Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
358 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 35. #3954 | C8 | semidirect |
| 185. C5 | #8294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×#170 | 2 |
| #10604695 | 2 |
| C2×#64879 | 2 |
| #10599709 | 2 |
| #10598787 | 2 |
| #8294 | 5 |